An Interior-Point Algorithm for Continuous Nonlinearly Constrained Optimization with Noisy Function and Derivative Evaluations

TL;DR

This paper introduces an interior-point algorithm for solving nonlinear constrained optimization problems using only noisy function and derivative evaluations, demonstrating effectiveness through numerical experiments.

Contribution

It develops a novel interior-point method that handles noisy function and derivative data, extending existing algorithms to more realistic, uncertain evaluation scenarios.

Findings

Algorithm effectively reduces stationarity measure despite noise

Numerical experiments show broad problem applicability

Performance remains robust under various noise levels

Abstract

An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy values of the objective and constraint functions and their first-order derivatives are available. The algorithm is based on a combination of a previously proposed interior-point algorithm that allows inexact subproblem solutions and recently proposed algorithms for solving bound- and equality-constrained optimization problems with only noisy function and derivative values. It is shown that the new interior-point algorithm drives a stationarity measure below a threshold that depends on bounds on the noise in the function and derivative values. The results of numerical experiments show that the algorithm is effective across a wide range of problems.